Detection of concealed object by standing waves

ABSTRACT

A process is provided to detect an object within a defined region using standing longitudinal cavity mode waves. The process includes disposing first and second conductive lines substantially parallel to the axis, transmitting an electromagnetic signal through the first line at a set frequency, returning the transmitted signal through the second line, measuring power from a reflected signal through the first line, adjusting the set frequency based on the measured power; extracting an appropriate parameter from the reflected signal to obtain a reflected characteristic, comparing the reflected characteristic to an established characteristic that lacks the object to obtain a characteristic differential, and analyzing the characteristic differential to obtain a position of the object along the length. The first and second conductive lines have specified length and width that bound a defined region. The analyzing can be performed by Fourier transform across wave modes.

CROSS REFERENCE TO RELATED APPLICATION

The invention is a Division, claims priority to and incorporates byreference in its entirety U.S. patent application Ser. No. 11/890,098filed Jul. 13, 2007, and issued Sep. 28, 2010 as U.S. Pat. No.7,804,441.

STATEMENT OF GOVERNMENT INTEREST

The invention described was made in the performance of official dutiesby one or more employees of the Department of the Navy, and thus, theinvention herein may be manufactured, used or licensed by or for theGovernment of the United States of America for governmental purposeswithout the payment of any royalties thereon or therefor.

BACKGROUND

The invention relates generally to methods and systems that use standingwaves to detect a buried or submerged object in an optically opaquemedium. In particular, the invention employs electromagnetic or sonicwaves and analyzes their standing wave patterns to identify the presenceand location of an otherwise hidden object having materialcharacteristics that differ from the medium into which the object isembedded.

Military personnel may be assigned to patrol regions where hostilecombatants operate. Concealed ordnance, e.g., landmine, improvisedexplosive device (IED), present a severe hazard of injury and/or deathin such reconnaissance roles. The difficulty in identifying, locatingand neutralizing such objects from a safe distance hampers efforts topacify these territories by elevating risk to travelers (especiallythose on patrol) well above acceptable levels.

SUMMARY

Conventional techniques to detect unauthorized intrusion yielddisadvantages addressed by various exemplary embodiments of the presentinvention. In particular, various exemplary embodiments provide amechanism to detect such target objects with greater safety distancemargins than conventionally available.

Various exemplary embodiments provide electromagnetic tomographyimplemented by spectral analysis in an excited Fabry Perot cavity todetect and locate enemy agents crossing security perimeters or buriedenemy ordnance, such as improvised explosive devices (IEDs) withinlocalized volumes such as the soil lying underneath roadways upon whichCoalition military vehicles must travel on a regular basis. Variantembodiments employ radio frequency electromagnetic waves or sonic waves,depending on application. Microwaves represent an exemplary portion ofthe electromagnetic spectrum in conjunction with microwave frequencycomputer-aided tomography (MCAT) implemented by spectral analysis.

Various exemplary embodiments provide methods and systems to detect anobject within a defined region using standing longitudinal cavity modewaves. The process includes disposing first and second conductive linessubstantially parallel to the axis, transmitting an electromagneticsignal through the first line at a set frequency, returning thetransmitted signal through the second line, measuring power from areflected signal through the first line, adjusting the set frequencybased on the measured power; extracting an appropriate parameter fromthe reflected signal to obtain a reflected characteristic, comparing thereflected characteristic to an established characteristic that lacks theobject to obtain a characteristic differential, and analyzing thecharacteristic differential to obtain a position of the object along thelength. The first and second conductive lines have specified length andwidth that bound a defined region. The analyzing can be performed byFourier transform across wave modes.

The two lines constitute a parallel-conductor radio-frequencytransmission line stub. The alternative embodiments further includestransmitting a swept radio frequency signal along the transmission line,measuring the frequency, amplitude, and width of the resonant modepeaks, comparing the frequencies, amplitudes and widths to thosepreviously obtained without target objects in the vicinity of thetransmission line, and Fourier transforming the difference therebycomputed.

These procedures may include recording the received signal by suitableinstruments to obtain a received frequency spectrum, comparing thereceived frequency spectrum to an established frequency spectrum withoutthe object, and Fourier transforming the difference to compute anintelligence function containing the target location.

BRIEF DESCRIPTION OF THE DRAWINGS

These and various other features and aspects of various exemplaryembodiments will be readily understood with reference to the followingdetailed description taken in conjunction with the accompanyingdrawings, in which like or similar numbers are used throughout, and inwhich:

FIG. 1 is a block diagram view of the system according to a reflectorembodiment;

FIG. 2 is a flowchart view of the signal analysis process for detectingan object;

FIG. 3 is a signal mode plot from an acoustic aquarium test;

FIG. 4 is a frequency band plot of an electromagnetic microwave signalwithout a target in the region (representing the cavity);

FIG. 5 is a frequency band plot of an electromagnetic microwave signalwith a target at the center of the region;

FIG. 6 is a position plot of an electromagnetic microwave signal with awooden target at the center of the region;

FIG. 7 is a position plot of an electromagnetic microwave signal with awooden target midway between the center and one end of the region;

FIG. 8 is a position plot of an electromagnetic microwave signal with ametal target quarter-way between the center and one end of the region;

FIG. 9 is a block diagram view of the system for a twin-lead embodiment;

FIG. 10 is an electric circuit diagram of a high impedance (opencircuit) condition for the twin-lead embodiment;

FIG. 11 is an electric circuit diagram of a low impedance (closedcircuit) condition for the twin-lead embodiment;

FIG. 12 is a mode plot of electric field vs. distance for the threelowest frequency transmission line modes for a closed or short circuitat the far end of the transmission line stub;

FIG. 13 is a mode plot of electric field vs. distance for the threelowest frequency transmission line modes for an open-circuit conditionat the far end of the transmission line stub;

FIG. 14 is a frequency shift plot based on target presence;

FIG. 15 is a frequency shift plot as a function of modes; and

FIG. 16 is a transform plot from modes to position.

DETAILED DESCRIPTION

In the following detailed description of exemplary embodiments of theinvention, reference is made to the accompanying drawings that form apart hereof, and in which is shown by way of illustration specificexemplary embodiments in which the invention may be practiced. Theseembodiments are described in sufficient detail to enable those skilledin the art to practice the invention. Other embodiments may be utilized,and logical, mechanical, and other changes may be made without departingfrom the spirit or scope of the present invention. The followingdetailed description is, therefore, not to be taken in a limiting sense,and the scope of the present invention is defined only by the appendedclaims.

Radar employs electromagnetic radiation to provide azimuth, elevationand range of an object. A transmitter projects radiation in themicrowave or radio spectrum. An object within line-of-sight of thetransmitter reflects a portion of the radiated energy, which proceeds asa traveling electromagnetic wave back, to a receiver, whereupon theradar system analyzes the reflected signal to obtain the desiredinformation. However, signal attenuation of short radiation wavelengths,at high frequencies, limit signal propagation and detection distances.For low frequencies, the object might escape detection if smaller thanthe long radiation wavelengths having less attenuation.

The object possesses material properties that differ from the concealingmedium. These properties influence real and/or imaginary portions of therefraction index at microwave frequencies, thereby indicating theobject's presence. A defined area of the medium may be interrogated withstanding waves that encompass a suitable range of wavelengths. Thestanding wave patterns contain integer numbers of nodes and antinodes,each of which is located at a known position along the cavity length.The object betrays its presence by selective absorption or scatter ofthe energy, rather than by reflection. The changes in energy, frequencyand quality associated with standing wave patterns (from an emptymedium) depend on the object's location.

The standing waves represent wavelengths related to the length of thearea being searched for the object's presence and location. The searcharea may be designated as a “cavity” having characteristic length L forthe distance between boundaries against which the waves reflect, such asa Fabry-Perot cavity. The wavelength λ=v/f, where f is frequency and vis the wave velocity for each longitudinal mode in the cavity has aquantized value that may be expressed as λ=2L/n, where n is a positiveinteger 1, 2, . . . N, and L is the cavity length. For anelectromagnetic wave, this velocity corresponds to nearly the speed oflight. For an acoustic wave, this velocity corresponds to thelongitudinal speed of sound, or additionally the transverse speed ofsound for a solid medium.

For the twin-lead application, the waves may be reflected at theboundaries of the search area to produce a node at the shorted end ofthe transmission line, an antinode at the open end of the line, and someinteger number of nodes and antinodes along the length of the line, theexact numbers being proportional to the frequencies of each standingwave mode. For a shorted far-end of the transmission line (closedcircuit), the transmission line length L must be an odd number multipleof a quarter wavelength λ for each mode. This can be expressed asL=(2n+1)λ/4, where n is a non-negative integer 0, 1, 2, . . . N. Theobject can perturb the standing wave either by shifting the frequency ofthe mode peaks, or by changing the amplitude of the power at the modepeaks.

Modern radar typically depends upon the reflection of very shortmicrowave-frequency pulses by a target of interest. Unfortunately, thepresence of microwave signals is recognized by many adversaries, some ofwhom have deployed buried or camouflaged ordnance with very small radarscattering cross sections and used it successfully against US forces inIraq and Afghanistan. The problem of locating, identifying, andneutralizing enemy agents and ordnance (particularly buried IEDs) at adistance has been a vexing challenge for US military analysts and amajor personal risk for Coalition warfighters.

Reflector Embodiment: Fortunately, recent developments in optoelectroniccomponent technology may be applied fruitfully to address problems suchas the detection of buried IEDs in arid Middle Eastern soil and thelocation of enemy agents crossing long security perimeters. An enemyagent or IED inherently contains substances that exhibit real and/orimaginary components of the index of refraction at audio, ultrasonic,radio, or microwave frequencies that do not precisely match those of thesurrounding air in which an agent may traverse or else the soil withinwhich an IED may be buried.

If such a target (operative or ordnance) can be interrogated with a setof standing radio waves that encompass a suitable range of wavelengths,the presence of the target causes absorption or scattering whosemagnitude is dependent upon the precise location of the target withrespect to the nodes and antinodes of each of the standing wave modepatterns. Thus the introduction of a target into a volume that has beenilluminated with a set of standing waves having an initially-uniformdistribution of power perturbs this distribution of power among thevarious wave modes. In addition, the frequencies and/or the quality ofthe standing wave modes may be perturbed by the presence of the targetobject.

This perturbation can be accurately measured with modern spectralanalysis instrumentation, and the location of the target can then beextracted from this perturbation by an appropriate type of mathematicalanalysis. Furthermore, this method of detection is most sensitive toobjects that are comparable to or smaller than the smallest wavelengthused to interrogate them and is therefore not subject to the usualdiffraction limit that affects conventional imaging technologies.

The detection algorithm (to be described subsequently) relies upon thedifferential absorption or scattering of a set of standing wave modepatterns and not upon the reflection of a narrow band of wavelengths asin traditional radar or imaging technology. This location technique canalso circumvent countermeasures to conceal hostile operatives orordnance by using stealth technologies that absorb electromagneticradiation in the radar frequency bands. The standing wave pattern can becreated by establishing a Fabry-Perot cavity in one or more physicaldimensions and exciting a set of standing wave modes within this cavityby use of a low power microwave transmitter. The cavity is formed byplacing two highly reflecting “mirror” surfaces at the ends of thedesired region to be protected and orienting them so that they areparallel.

This ensures that waves with propagation directions parallel to thecavity axis may travel back and forth within the cavity and experiencemultiple reflections at the two mirror ends. In order to ensure that alarge set of modes is excited within the cavity, the transmitter sweepsoften over a sufficiently wide bandwidth to encompass the desired rangeof wavelengths. For the various embodiments presented herein, theinstant disclosure proposes the exploration of a new technology thatexploits the differential absorption and/or scattering of a set ofstanding waves to detect and locate accurately a concealed target andpresents results from two preliminary trials of the technology.

Diagram: FIG. 1 shows a block diagram 100 of the detection system. Agenerator 110 provides an electromagnetic wave signal to a transmitter120, which projects the signal through a transmit antennas 130 to beintercepted by a receive antenna 135, with both antennas (e.g.,transducers or horns) being embedded within a cavity 140. The signalpropagates within the cavity 140 through a medium (e.g., air, soil,water) along a longitudinal axis 145. The cavity 140 is bounded at eachend by corresponding reflectors 150, 155 (e.g., microwave mirrors).Frequencies of the signal received by the receive horn 135 are evaluatedby a radio frequency (RF) signal analyzer 160 and further processed by acomputer 170, which may illustrate the resulting modes on a displaymonitor 175. By monitoring the frequency modes, a change thereinindicates the presence of a target 180, shown as a buried IED.

The reflectors 150, 155 are oriented parallel to each other, beingdisposed at the longitudinal ends of the cavity 140, which represents aregion to be monitored. The longitudinal cavity axis 145 is formed by aline perpendicular to the reflectors 150, 155 that extends the distancelength of the cavity 140. These mirrors may be flat or parabolicallycurved to focus the reflected waves.

The transmitter 120 may transmit microwaves at low power, and thesemicrowaves are frequency-swept by modulation generator 110 for sendingto the transmit antenna 130. This transmit antenna 130 would generallybe implemented as an electromagnetic horn, possibly with some gain overan isotropic radiator to confine most of the radiation to the directionof the cavity axis 145.

The power generated by the frequency-swept transmitter 120 is injectedthrough the transducer 130 and into the cavity 140 as electromagneticradiation. This power may be attenuated because some waves are emittedin directions that are not parallel to the cavity axis 145. Thatfraction of the power in waves that run parallel to the cavity axis 145travel back-and-forth between the two reflectors 150, 155 and resonatewithin the cavity 140 at all discrete frequencies for which the cavitylength L is an exact integer multiple of a half-wavelength.

These standing waves interact with the target 180, which willselectively absorb or scatter some of the cavity modes. As a result, theoverall shape of the spectrum is perturbed by the presence of the target180. This perturbed spectrum can be detected by receive antenna 135 andanalyzed by the spectrum analyzer 160, which sends its information tothe computer 170 through an appropriate interface (e.g., GPIB, USB) andprocessed by a suitable program. The computer 170 analyzes the spectralshape using an algorithm presented further herein. As a result of thisanalysis, the computer 170 extracts from the spectral shape anintelligence function that is displayed on the monitor 175. Thehorizontal axis of this plot represents distance, and the vertical axisrepresents deviation from average cavity materials properties. Thetarget 180 is thus represented by a peak in the monitor 175 thatresembles the blip on a traditional radar range scan.

Process: FIG. 2 illustrates a flowchart 200 that describes the analysisand procedure for receiving and processing the standing wave signals todetect an intrusive object within a defined region. An iterative step210 provides data resulting from the measurement of the power,frequencies and/or quality (denoted as Q) for each of a suitably largenumber of longitudinal cavity modes. Previously acquired data underconditions absent any target are acquired and stored at step 220. Theseresults from step 210 are compared at step 230 with the correspondingdata from step 220.

The algebraic difference between these two data sets, computed at step230, are then subjected to the Discrete Fourier Transform at step 240.The magnitude of the output data set from step 240 is computed in step250 and either displayed for observation by a human operator and/oranalyzed by the software for automatic detection of target peaks. Aftera suitable period of time, the process is repeated, and the program flowreturns to step 210 to begin the analysis of the next set of dataacquired by the receiver.

Algorithm: The mathematical details of a microwave frequencycomputer-aided tomography (MCAT) Algorithm used to process the receivedspectrum and extract therefrom the intelligence function that bearsinformation on the location of targets of interest. This detectionsystem relies upon the creation of a Fabry-Perot cavity that bounds thecavity 140 that defines the spatial region. This cavity 140 consists oftwo parallel mirrors 150, 155, separated by a longitudinal distance L.

One of the well-known properties of such cavities is that standing wavescan resonate in the region between the mirrors 150, 155 only at thosediscrete frequencies for which the cavity length L is an integralmultiple of a half wavelength;

$\begin{matrix}{{L = \frac{m\;\lambda_{m}}{2}},} & (1)\end{matrix}$where λ_(m) is the wavelength of the longitudinal cavity mode for whichm half wavelengths exactly fit in the region between the reflectors. Forthis example, the cavity length L is in the range of 10 km (kilometers).Specific field-deployable implementations of this invention may utilizecavity lengths ranging from tens of meters to tens of kilometers.

Artisans of ordinary skill will recognize that the frequency separationδf between adjacent longitudinal modes is given by the expression:

$\begin{matrix}{{{\delta\; f} = \frac{c}{2\;{nL}}},} & (2)\end{matrix}$where c is the speed of light in vacuo, and n is the index ofrefraction. For n=2 as a reasonable value for soil in the arid climatesof the Middle East at low microwave frequencies, the adjacent modalseparation is in the neighborhood of 7.5 kHz (kilo-Hertz), a valueeasily resolved with modern microwave spectrum analyzers.

This Fabry-Perot cavity can be excited by a low-GHz (giga-Hertz)frequency microwave transmitter 120 via the transmit horn (or othersuitable antenna) 130 to carry the transmitter's signal in the cavity140. The transmit antenna 130 may preferably be disposed in closeproximity to one of the two parallel reflectors 150, both disposedwithin the soil of the region comprising the cavity 140. For thetransmitter 120 being frequency-swept by the generator 110 over abandwidth of 130 MHz in a low GHz band, the resulting band-width may besufficient to encompass about 17,300 longitudinal modes, eachdistinguished by the 7.5 kHz modal separation interval.

Assuming that signal losses associated with absorption in the medium(e.g., soil) are not excessive, these longitudinal modes lying withinthe frequency-swept bandwidth of the transmitter 120 may resonate withinthe cavity 140. These cavity modes may be detected by the receiveantenna 135 placed in the soil near the other reflector 155 andconnected to the RF spectrum analyzer 160.

Quantifying the energy present in each of these longitudinal modes canbe achieved by a set of traditional first-order rate equations. Theseare similar to the rate equations for a semiconductor laser, butmodified slightly to make them applicable to the geometry in FIG. 1. ForS_(m) being the number of photons-per-cubic-meter associated with them^(th) longitudinal mode (i.e., amplitude), α_(m) is the loss associatedwith the same mode, P_(t) being the RF power output of the microwavetransmitter, and C_(m) being the probability-per-unit-time of exciting aphoton in the m^(th) longitudinal mode, the rate of change in photondensity for the m^(th) mode may be written as follows:

$\begin{matrix}{\frac{\mathbb{d}S_{m}}{\mathbb{d}t} = {{C_{m}P_{t}} - {\frac{c}{n}\alpha_{m}{S_{m}.}}}} & (3)\end{matrix}$

The spectrum analyzer 160 may be used to measure the relative amplitudeS_(m) of each longitudinal mode. To model signal loss as a function ofwavelength, an analogy to first order laser gain may be applied. Thisfirst order laser gain is modulated by the first moment of the spatialgain with respect to the square of the longitudinal mode electric fielddistributions. See, e.g., Yamada, M. and Suematsu, Y., “Analysis of GainSuppression in Undoped Semiconductor Lasers”, J. Appl. Phys., 52,2653-2664, (1981).

This insight was applied for various exemplary embodiments in creatingthe software for the laser Defect Distribution Scan Algorithm. See,e.g., DeChiaro, L., Robinet, M., and Devoldere, P., “Effects of DriveCurrent Upon Defect Distribution Scan Features in Multi-longitudinalMode Semiconductor Lasers”, J. Lightwave Technology, 11, 2057-2065,(1993). The same principle may be extended to the presence of a targetof interest such as a concealed enemy agent or a buried IED. Due to thevarious internal constituents, the presence of the target may create asharply-localized perturbation in the real and/or the imaginarycomponents of the index of refraction of the surrounding medium.

The physical size of the target 180 may be sufficiently small so as toexhibit a negligible scattering cross section at low microwavefrequencies. Nonetheless, its presence yields a frequency-selectiveattenuation of some of the longitudinal modes, depending upon its exactlongitudinal coordinate relative to the nodes and antinodes of the modalelectric field distributions. Thus, the loss for the m^(th) longitudinalmode may be modeled as follows:

$\begin{matrix}{{\alpha_{m} = {\alpha_{0} + {\int_{0}^{L}{{G(z)}{{E_{m}(z)}}^{2}{\mathbb{d}z}}}}},} & (4)\end{matrix}$where α₀ is the constant background loss, G(z) is thespatially-dependent loss (i.e., intelligence function) represented byany perturbations of the cavity medium (including IEDs, buried rocks,subterranean tunnels, or foliage), and E_(m) (z) is the electric fielddistribution of the m^(th) mode.

For the spectrum analyzer 160 able to measure values of photon densityS_(m) for many excited cavity modes, eqns. (3) and (4) may be solved bya simple Fourier Transform method to obtain the intelligence functionG(z). In steady state, all the time derivatives in the system for eqn.(3) vanish, and eqn. (3) may then be solved for the steady statespectrum to obtain:

$\begin{matrix}{S_{m} = {\frac{{nC}_{m}P_{t}}{c\left( {\alpha_{0} + {\int_{0}^{L}{{G(z)}{{E_{m}(z)}}^{2}{\mathbb{d}z}}}} \right)}.}} & (5)\end{matrix}$

Next, the cavity losses may be postulated as not being exceedinglylarge. For such a condition, the modal electric field distribution canbe approximated as follows:

$\begin{matrix}{{E_{m}(z)} = {\sin\;{\frac{2\;\pi\; z}{\lambda_{m}}.}}} & (6)\end{matrix}$

Substituting eqn. (6) in the integral in the denominator of eqn. (5) andrecalling the trigonometric identity sin²θ=(1−cos2θ)/2, eqn. (5) reducesto:

$\begin{matrix}{{S_{m} = \frac{{nC}_{m}P_{t}}{c\left( {\alpha_{0} + \frac{L\overset{\_}{G}}{2} + {\frac{1}{2}{{\hat{G}}^{+}(\lambda)}}} \right)}},} & (7)\end{matrix}$where G is the spatial average of G(z) and Ĝ⁺ (λ) is the InverseDiscrete Fourier Transform of the intelligence function G(z), using thesine functions of the modal electric fields of eqn. (6) as Fourier basisfunctions for the series expansion.

Because L and G are both constants, the second term in the denominatorof eqn. (7) may be combined into the α₀ term with no loss of generality.Eqn. (7) can be solved to yield Ĝ(λ), and the intelligence function G(z)retrieved by a Fourier Transform as follows:

$\begin{matrix}{{{G(z)} = {F\; F\;{T\left\lbrack {\frac{2\;{nC}_{m}P_{t}}{{cS}_{m}} - {2\;\alpha_{0}}} \right\rbrack}}},} & (8)\end{matrix}$where FFT designates the Discrete fast-Fourier Transform (FFT)operation.

In order to implement eqn. (8) in software, the parameters remaindefined as: S_(m) is the discrete spectrum measured by the analyzer,P_(t) is the average RF power supplied by the transmitter, C_(m) is theprobability-per-unit-time of photon emission into the m^(th)longitudinal mode, n is the average index of refraction of the cavitymedium, c is the speed of light in vacuo, and α₀ is the background lossof the cavity medium.

The C_(m) probabilities are given by the shape of the radiated emissionspectrum of the continuous wave (CW) microwave transmitter and antennacombination. For a reasonably flat frequency response of thiscombination, the values of C_(m) should be constant over a bandwidthsufficiently large to encompass about 16,384 longitudinal modes.

The choice of a number of modes that is an integral power of two is madein order to permit the use of the fastest possible softwareimplementation of the Cooley-Tukey Algorithm to perform the Fouriertransformation and retrieve the intelligence function G(z) in minimaltime. See, e.g., Cooley, J. W. and Tukey, J. W., “An Algorithm for theMachine Calculation of Complex Fourier Series”, Mathematics ofComputation, 19, 297-301, (1965).

In practice, the negative term on the right hand side of eqn. (8) shouldappear as a direct current (DC) level upon which thewavelength-dependent perturbations associated with the targets ride.This term can therefore be suppressed before the Fourier transform isdone. Such practices may enhance the overall numerical sensitivity ofthe software.

Typically, a function is solved by transform of its inverse, as providedin eqn. (8). However, for results obtained for this intelligencefunction application, solving by FFT of the function may improvesensitivity for a small target. Thus, the intelligence function G(z) maybe alternatively expressed as a Fourier transform of the differencebetween the photon density S_(m) for each mode m and a reference valueS_(0m) absent any target. This can be expressed as:G(z)=FFT[S _(m) −S _(0m)].  (9)

Acoustic Tests: The MCAT Algorithm may be applied to a wide variety ofwave phenomena. A preliminary feasibility test of the concept wastherefore accomplished with a minimal investment by running a trialusing ultrasonic acoustic water waves in a volume sufficiently small fordemonstration purposes. The protected region and the cavity mirrors wereboth realized by an aquarium (i.e., fish tank) filled with tap water.The glass walls of the tank are very parallel and reflect sound waves.

Because the short dimension of the tank measured about 0.15 m (meter)and the speed of sound in fresh water is taken to be 1435 m/sec(meters-per-second), the modal separation may be computed from eqn. (2)to be 4.78 kHz. Thus, the demonstration used ultrasonic frequencyequipment. A low-power function generator such as the Hewlett-Packard(HP) 8111A was chosen for the transmitter 120, and an ICOM PCR1500 radiocommunications receiver was used as the spectrum analyzer 160. (ThePCR1500 is a computer-controlled receiver whose supplied softwareincludes a spectrum analyzer mode and a data recorder function that usesthe hard drive of the controlling computer to store the acquiredspectra). Low cost piezoelectric transducers were used as the transmitand receive antennas 130, 135.

The signal generator 110 was configured to generate square waves, andthe frequency was adjusted to a value close to 4.78 kHz so that theharmonics would fall at the cavity mode frequencies. The PCR1500 was setto scan the frequency range from 50 kHz to 250 kHz and record thespectra measured with and without a target 180 in the cavity 140.

FIG. 3 illustrates a plot 300 from these acoustic tests. This graphfeatures frequency f up to 300 kHz as the abscissa 310 and signalstrength in arbitrary units (au) as the ordinate 320. The graph showstwo example spectra: a solid line 330 representing measurements withouta target, and a dash line 340 representing measurements in which thetank includes a ball-point-pen-tip inserted into the water near the tankcenter. Some of the modes show signal strength differences 350 betweenthe respective measurements. A sharp spike near 250 kHz is caused by aspurious response with the receiver.

An example peak 360, such as at 170 kHz illustrates several additionaldetails. Its peak strength of ˜190 au may be used to determine afrequency resolution (i.e., peak width), denoted as Δf, that representsthe frequency difference of the peak 360 at its half peak strength 370.The frequency difference between the peak 360 and its nearest spectralneighbor represents free spectral range (FSR), quantified as v/4d. TheFSR may be represented by a frequency difference 380 between modalpeaks. (For electromagnetic waves, velocity v is analogous to the speedof light c.) The cavity 140 may be characterized by quality denoted asQ=f/Δf, and “finesse” quantified as FSR/Δf.

Compared with the empty cavity spectrum, the spectrum measured with thetarget in place shows a perturbed shape in which every other mode isenhanced, while the intervening modes are attenuated. The spectraldeviation caused by the presence of the target 180 is thus described asa “strong-weak-strong-weak” pattern that is characteristic of a cavitywith a perturbation (denoting the target) located at the cavity'smid-position. The period of the spectral deviation is the minimummeaningful value of two mode spacings.

Electromagnetic Tests: The observation of acceptable results from theacoustic test demonstrated the feasibility of the tomography concept.Subsequent trial would involve electromagnetic waves sent through airover a path length that is measured in meters rather than centimeters.Such tests were performed using the large anechoic chamber at Dahlgrenwith a cavity length of 10 m (meters). An Agilent E8251A signalgenerator was used as the transmitter.

The best results for these tests were obtained over the 4 GHz to 5 GHzfrequency range, using microwave horns as the transmitting and receivingantennas 130, 135. The transmitter 120 was set to cover the frequencyband in steps of 1 MHz with a dwell time of 1 s (second) at eachfrequency. The reflectors 150, 155 were two rectangular pieces of sheetaluminum measuring about 0.6 m-by-1.0 m to act as microwave mirrors.Power levels were about +11 dBm at the transmitter output connector.

A 15 m length of coaxial cable was used between the transmitter outputand the transmit antenna. In the 4 GHz to 5 GHz band, this cableexhibits an estimated 8 dB (deci-Bell) loss. Thus, the actualtransmitter power at the antenna 130 is estimated to be about +3 dBm(deci-Bell-milliwatt). The transmit and receive antennas 130, 135 wereplaced in the cavity 140 about 15 cm (centimeters) from the reflectors150, 155 and oriented so that the microwave beams were directed at thereflectors in order to minimize the signal sent directly from transmitto receive antennas.

Signal reception was implemented by an Agilent E4407B spectrum analyzerand was controlled by a legacy Dolch 486 computer equipped with an HPGPIB interface card. Applications programming was done in the ASYSTprogramming language for reasons of convenience and cost. The E4407B wasset to cover the 4 GHz to 5 GHz range. Resolution and video 3 dBbandwidths were each set to 100 kHz, and the time per scan was about 200ms (milliseconds). The E4407B was programmed to identify the strongestpeak in each scan and to report the frequency and strength to thecomputer 170.

FIG. 4 shows a plot 400 of the spectrum measured in the absence of anytarget 180. This graph features frequency between 4 GHz and 5 GHz as theabscissa 410 and received power in dBm as the ordinate 420. A continuousline 430 represents the power for each frequency without a target withinthe anechoic chamber that defined the cavity 140. The analyzer noisefloor was about −72 dBm, and the spectrum consists of about 872 datapoints.

Received signal strength varied between −43.5 dBm and −51.5 dBm,providing a margin of about 20 dB above the analyzer noise floor. Theplot 400 shows considerable structure on both large and small scales.The small scale structure of the line 430 consists of a series of small,regularly-spaced peaks that are separated by about 15.7 MHz on average.This agrees well with the value of 15 MHz that is predicted by eqn. (2)for an air cavity with a length of 10 m. These peaks are therefore thelongitudinal mode peaks of the cavity that are necessary for the MCATAlgorithm to operate properly.

The large scale structure also shows evidence of periodic behavior witha period of about 430 MHz in frequency space. This structure is believedto originate in a physical process different from the cavity resonancesthat give rise to the longitudinal modes mentioned above. One possiblecandidate mechanism is resonances associated with the feed-hornantennas. These will invariably exhibit some frequency dependence intheir radiation pattern, and variation of the main lobe size by a few dBfrom 4 GHz to 5 GHz is not unreasonable.

Another possibility, however, is that the very presence of the transmitand receive horns 130, 135 and the coaxial cable feed-lines in thecavity 140 can perturb the field configurations due to the scattering ofthe waves. Thus, the MCAT scans may provide information on any and allobjects in the cavity whose real or imaginary parts of the index ofrefraction differ from those of air. Given the present physical designof our system, this specifically includes the two antennas and somefractional length of their coaxial feed-lines. Additionally, thepeak-to-valley contrast of the modes varies between 1 dB and 2 dB can beobserved from FIG. 4. Clearly, this contrast is preferably to be aslarge as possible in order to provide an improved level of sensitivityto a weakly absorbing or reflecting target. This contrast is related tocavity quality Q, related to resolution, and finesse, related to dampingtime.

The cavity quality Q may be increased by minimizing losses. This processwould include spillover losses from the feed-horns (if the reflectorssubtend a solid angle smaller than that of the main lobes), as well asdiffraction losses and losses due to mirror misalignment and the finiteconductivity of the reflector material. Careful engineering design canminimize most of these, and this portends subsequent opportunities toimprove the performance and sensitivity of future systems.

Despite the modest modal contrast shown in FIG. 4, the introduction of atarget 180 into the microwave beam resulted in a measurable perturbationof the power distribution among the longitudinal cavity modes. FIG. 5shows the spectrum that was measured after a wooden object (i.e., target180) was placed in the cavity within the microwave beam. The portion ofthe target 180 that was intercepted by the microwaves consists of asingle wooden 2×4 plank (i.e., stud) oriented vertically (i.e., uprightand hence transverse to the ground surface) with the short dimensionparallel to the cavity axis 145.

This caused an overall drop of about 2 dB in the measured signalstrength across the 4 GHz to 5 GHz band. More important, the presence ofthe target (in the anechoic chamber) also introduced a perturbation intothe modal structure so that the modes exhibited the samestrong-weak-strong-weak pattern of oscillations that is shown in thewater wave graph of FIG. 3 for the fish tank. This represents thespectral signature expected for a target 180 placed in the center of thecavity 140.

In particular, FIG. 5 shows the received spectrum as a plot 500 with theupright wooden 2×4 plank disposed in a 10 m cavity 140 at a positionnear the center at 5 m from either end. This graph features frequencybetween 4 GHz and 5 GHz as the abscissa 510 and received power in dBm asthe ordinate 520. A continuous line 530 represents the power for eachfrequency with the plank target near the center the anechoic chamberthat defined the cavity 140. In order to display this positioninformation in a quantitative manner, the spectral perturbations causedby the target must be extracted. This can be accomplished by identifyingthe frequencies of the mode peaks in the unperturbed data of FIG. 4,examining the same frequencies in the FIG. 5 data, subtracting away theunperturbed spectrum, and Fourier transforming the difference. Theresults are shown in FIG. 6.

In particular, FIG. 6 shows the resulting MCAT scan of thisconfiguration with the upright wooden 2×4 plank disposed at the cavitycenter. This graph features distance from the cavity's boundary edge inmeters as the abscissa 610 and return strength in arbitrary units as theordinate 620. A continuous line 630 denotes the deviation from averagecavity materials properties caused by the plank target as a function ofposition along the length of the cavity. The “radar return” from thetarget 180 denoted by an arrow 640 is shown at the right side of theplot 600. This indicates an abrupt change in the materials propertiesintercepted by the microwave beam at the center of the cavity (i.e., the5 m position of the 10 m cavity length). The large difference feature atthe left side of the plot 600 is believed to be an artifact causedeither by the antenna horn resonances or by the modal perturbationsinduced by the presence of the two horn antennas in the cavity.

Other target configurations were also investigated to ensure that theMCAT Algorithm faithfully responds to different target locations. FIG. 7shows a plot 700 of the MCAT scan for the same upright wooden 2×4 plank,but disposed about 3 m from the receiver reflector 155. This graphfeatures distance from the cavity's boundary edge in meters as theabscissa 710 and return strength as the ordinate 720. A continuous line730 denotes the deviation from average cavity materials propertiescaused by the plank target as a function of position along the length ofthe cavity. The target's location is denoted by an arrow 740 shown nearthe center of the plot 700

FIGS. 6 and 7 illustrate the sensitivity of the MCAT system to targetsthat are composed primarily of dielectric materials (e.g., wood). Todeploy an MCAT network to detect buried IEDs or land mines, however, thesystem must demonstrate response to metallic objects also. In order toshow this capability, a second target consisting of avertically-oriented (i.e., upright) metal pipe supported at the bottomby a circular, metallic base was disposed in the cavity at a distance of1.6 m from the receiver reflector 155, and spectra were acquired. Theresultant MCAT scan is shown in FIG. 8.

In particular, FIG. 8 shows a plot 800 of the MCAT scan for the metalpipe and base, disposed about 1.6 m from the receiver reflector 155.This graph features distance from the cavity's boundary edge in metersas the abscissa 810 and return strength as the ordinate 820. Acontinuous line 830 denotes the deviation from average cavity materialsproperties caused by the plank target as a function of position alongthe length of the cavity. The target's location is denoted by an arrow840, shown near the 1.5 meter position along the cavity length in theplot 800.

Application: The first application of the tomography algorithm describedherein was developed for the location of atomic scale crystallographicdefects lying within the active layers of semiconductor lasers. Thecavity lengths of such low power communications lasers are typically inthe neighborhood of 250 μm (micrometers). The successful application ofthis algorithm to the 15 cm fish tank required that the algorithm bescaled up by a factor of about six-hundred from the laser scales. Thesecond step upward to our 10 m anechoic cavity involves a total scalingfactor of about forty-thousand from the laser length scales. Toincorporate the MCAT Algorithm on the battlefield would typicallyrequire an additional increase in scale by about an additional factor ofa thousand, or three orders of magnitude.

This factor of a thousand can be accomplished in approximately threefurther steps. The first of these would involve a cavity length of 150meters and will take place near the flight line in the Maginiot Open AirTest Site (MOATS) Facility at Dahlgren. Pending approvals by BaseOperations, Safety, and the Flight Line organizations, the second stepwould involve a path of 1500 m and may be performed adjacent to theDahlgren Flight Line. The final scale-up to a 10 km path and thetransition to an underground path will need to be accomplished at anoff-base facility such as Yuma, Ariz. where the testing of a 10 km MCATwill not interfere with other activities and the soil is sufficientlydry to approximate conditions in the Middle East.

The system described herein could be deployed as an automated network ofsensors, spaced at regular intervals along a roadway of interest. Forexample, the straight line distance from Baghdad to Tikrit is about 159km. If there were a road running directly between the cities andassuming that a separation of 10 km between neighboring stations yieldsacceptable sensitivity and spatial resolution in the Iraqi soil, thenthis road would be divided into sixteen segments, each of 10 km inlength, and thus employ seventeen sensor stations, the first equippedwith one transmitter and a mirror, and the last equipped with onereceiver and a mirror. The fifteen stations along the roadway would eachemploy two reflectors, one transmitter, and one receiver.

The computers controlling each receiver would be programmed to commandthe local spectrum analyzer to measure an RF spectrum at periodicintervals such as every 5 minutes. Each spectrum would be uploaded tothe local controlling computer, which would then process the dataaccording to the algorithm, extract the intelligence function, andcompare that with intelligence functions extracted from previous scansmeasured from the same volume of soil.

If the software determines that a significant, new peak suddenly appearsin one of the sixteen straight road segments between Baghdad and Tikritand remains stable for a predetermined period of time, the computer 170would be programmed to automatically raise an alarm and relay thecoordinate information of the new signal peak to Coalition personnel,who can then dispatch appropriate forces to take action as determined bythe local commanding officer.

In summary, microwave frequency computer-aided tomography (MCAT) can beimplemented by spectral analysis in an excited Fabry Perot cavity as ameans of detecting and locating hostile agents crossing securityperimeters or buried enemy ordnance such as IEDs within localizedvolumes such as the soil lying underneath roadways upon which Coalitionmilitary vehicles must travel on a regular basis.

This disclosure presents a description of the fundamental principlesupon which such a detection system is based and contains the results oftwo trials of the system; the first implemented with ultrasonic acousticwaves in a 15 cm fish tank and the second with microwaves in a 10 mcavity housed within an anechoic chamber. We report the computation ofMCAT scans containing peaks whose locations correspond accurately to thetarget positions for targets composed of wood and metal. These resultsindicate technical feasibility to extract from measured cavity spectraan intelligence function giving the locations of inhomogeneities lyingwithin the cavity, particularly buried IEDs.

Twin-Lead Embodiment: In an alternative embodiment, the attenuation ofthe medium can be circumvented by stretching a pair of parallel wiresalong a distance L and across a width W to be interrogated. It is alsopossible to use existing local infrastructure such as overhead powerlines to implement a sensor under the proper conditions.

FIG. 9 illustrates a block diagram 900 showing the twin-leadconfiguration. A signal oscillator 910 provides a tuned alternatingcurrent (AC) (AC) signal along the parallel conductor transmission linecomprised by wires 920 and 930. The wire leads 920, 930 stretch alongthe distance L and separated by the width W to a terminus 940 enclosinga target 950. Depending on the configuration of the circuit, theterminus 940 may be open or closed. The characteristic impedance of theparallel conduction transmission line may be represented by therelation:

$\begin{matrix}{{Z_{0} = {276\;{\log_{10}\left( \frac{2W}{a} \right)}}},} & (10)\end{matrix}$where Z₀ is the impedance in Ω(ohms), W the spacing width between thewires and a is wire diameter, both lengths in comparable units. As canbe observed from eqn. (10), impedance increases with increasing widthand decreasing wire diameter.

For the terminus 940 being open, the system 900 represents a shunt oropen loop, which can be schematically described as a parallelinductor-capacitor circuit. This shunt signal is reflected at theterminus 940. For the terminus 940 being closed, the system 900represents a short circuit at the terminus 940 so that impedance remainszero at all frequencies. This short signal is bounded at the terminus940, which may include a power meter, while the circuit at oscillator910 remains open.

FIG. 10 shows an electrical schematic 1000 for the parallelinductor-capacitor circuit (also known as a “tank” circuit) that behavesas an open circuit or shunt. The oscillator 910, represented by nodes1010 are connected by a circuit 1020 that includes an inductor 1030 anda capacitor 1040 connected together in a parallel loop 1050, therebycausing high impedance at resonance. FIG. 11 shows an electricalschematic 1100 for the series inductor-capacitor circuit that behaves asa low impedance or near short circuit at resonance. The oscillator 910,represented by nodes 1110 are connected by a circuit 1120 that includesan inductor 1130 and a capacitor 1140 connected together in series. Thisbehaves as though the oscillator had been terminated with a seriesresonant inductor-capacitor circuit representing the transmission linestub.

The closed circuit, with the terminus 940 representing a closed switch,reflects waves as odd harmonics of the quarter wave-length defined bythe distance L. As described previously, each closed circuit wavelengthλ in the cavity has an harmonic expressed as L=(2n+1) λ/4, where n is anon-negative integer 0, 1, 2, . . . N. These harmonics are shown in FIG.12 as a plot 1200 for three lowest values of n. This graph featuresnormalized distance between the oscillator 910 and the terminus 940 asthe abscissa 1210 and wave amplitude as the ordinate 1220. The plot 1200shows harmonic cosine curves for n=0 as solid line 1230, n=1 as dashline 1240 and n=2 as dot-dash line 1250. Vertical lines are shown atabout ⅓ and ⅝ of distance L at 1260 and 1270, respectively.

As can be observed, the first line 1260 shows high (absolute) amplitudesfor the first and third harmonic curves 1230, 1250, but is negligiblefor the second harmonic curve 1240; and the second line 1270 showshigh-to-moderate amplitudes (e.g., received power) for the first andsecond harmonic curves 1230, 1240, but is negligible for the thirdharmonic curve 1250. These differences can be exploited by a spectrumanalyzer to determine amplitude differences induced by a target'spresence.

In particular, a target located at ⅓ L may absorb the electromagneticenergy for the first and third wave modes (having non-zero magnitudes),but not the second mode (having substantially no magnitude).Alternately, for the target position at ⅝L may absorb theelectromagnetic energy for the first and second modes, but not the thirdmode. Evaluation of additional modes enables intermediate positionswithin the modal region to be compared. The different levels ofabsorption depending on which modes are affected provides an indicatorof the target's location. In this quarter wave example, the transmissionline stub appears as a resonant circuit in which the capacitiveimpedance component is given by Z_(C)=−j/(2πfC), where C is thecapacitance per unit length of transmission line, f is frequency, andj=√−1 represents the imaginary coefficient.

Similarly, each open circuit wavelength λ in the cavity has an harmonicexpressed as L=(n+1)λ/2, where n is a non-negative integer 0, 1, 2, . .. N. These harmonics are shown in FIG. 13 as a plot 1300 for threelowest values of n. This graph features normalized distance between theoscillator 910 and the terminus 940 as the abscissa 1310 and waveamplitude as the ordinate 1320. The plot 1300 shows harmonic cosinecurves for n=0 as solid line 1330, n=1 as dash line 1340 and n=2 asdot-dash line 1350. Vertical lines are shown at about ⅛, ½ and ¾ ofdistance L at 1360, 1370 and 1380, respectively.

As can be observed, the first line 1360 shows high-to-moderate(absolute) amplitudes for the first and second harmonic curves 1330,1340, but is negligible for the third harmonic curve 1350. The secondline 1370 shows high amplitude for the second harmonic curve 1340, butis negligible for the first and third harmonic curves 1330 and 1350. Thethird line 1380 shows high-to-moderate amplitudes for the first andthird harmonic curves 1330, 1350, but is negligible for the secondharmonic curve 1340.

In particular, a target located at ⅛L may absorb the electromagneticenergy for the first and second modes, but not the third mode.Alternately, for the target position at ½ L, the electromagnetic energymay be absorbed for the second mode, but not the first and third modes.Similarly, the target at ⅛L may absorb at the first and third modes, butnot the second mode. These differences can be exploited by a spectrumanalyzer to determine amplitude differences induced by a target'spresence. The open circuit represents a high-impedance circuit withZ_(L)=j2πfL.

A circuit's impedance is a complex quantity (i.e., having real andimaginary components) that can be more generally expressed by therelation

$\begin{matrix}{{Z = {{R + {j\left( {{2\pi\;{fL}} - \frac{1}{2\pi\;{fC}}} \right)}} = {R + Z_{L} + Z_{C}}}},} & (11)\end{matrix}$where R is the real component resistance. At low frequencies, the Z_(C)term in eqn. (11) dominates so that the circuit appears capacitive. Athigh frequencies, the Z_(L) term in eqn. (11) dominates so that thecircuit appears inductive. At the natural or resonant frequencyf_(r)={2π√(LC)}⁻¹ for the parallel circuit in FIG. 10, the Z_(C) andZ_(L) terms cancel, producing a pure resistance circuit having noimaginary component. The presence of a target in the vicinity of thetransmission line sensor alters either the real and/or the imaginarycomponents of the transmission line impedance. The changes so producedmay vary as a periodic function of the mode number being measured. Theexemplary embodiments provide for detection of a target despite itsconcealment by signal absorption.

Resolution of the target's presence by the signal analyzer 160 may bedetermined by various methods, such as comparing amplitudes of peaks ofsignals with and without the target's influence 340, 330 for selectharmonic frequencies, as described for FIG. 3. Alternatively, the signalanalyzer 160 may determine a frequency offset for conditions of adequatequality and finesse. FIG. 14 shows a plot 1400 with frequency f as theabscissa 1410 and wave amplitude as the ordinate 1420. The plot 1400features a nominal inverse cosine function wave 1430 and an offsetinverse cosine function wave 1440 influenced by the target for a singlemode. The nominal wave has peak amplitude at a first frequency 1450, andthe offset wave has peak amplitude at a second frequency 1460, the twofrequencies being offset by a frequency difference Δf shown as a gap1470. This offset can be determined for each mode over a series tocharacterize the absorption and reflection characteristics of thetarget.

The frequency difference Δf can then be plotted over a series of modesto thereby determine the pattern of shifts induced by the target.Information on the target location is contained within the pattern. FIG.15 shows a plot 1500 with mode numbers as the abscissa 1510 andfrequency difference Δf as the ordinate 1520. As can be observed, thevalue of the frequency shift is a periodic function of the mode number,and both positive and negative shifts are observed. This frequency shiftis shown in this example to vary as a sinusoidal wave 1530 havingpositive maxima 1540 and negative minima 1550 at the extrema. Thesinusoidal wave 1530 illustrates a continuous curve produced from acollection of discrete values for each mode. At the inflection points1560, the frequency shift reaches zero, reflecting modes with resonantfrequencies unperturbed by the target. The slope 1570 at the inflectionpoints 1560 provides a measure of the maximum rate of change infrequency shift with respect to transmission line mode number.

As the slope 1570 increases (i.e., becomes steeper), the target may bemoving closer to the center of the cavity of the twin-lead configuration900 along its longitudinal axis, or the target may be moving closer tothe transmission line conductors 920, 930 themselves. A power meter thatinductively senses the current through the transmission line 920 of thetwin-lead circuit 900 may provide the output signal to be analyzed by asuitable instrument, such as a power meter or a spectrum analyzer. Themodal curve has a wavelength or period 1580 that corresponds to thetarget's position with respect to the cavity ends. For a target aboutmid-way between the ends of the cavity, the corresponding wavelength isshort, providing rapid peak-to-peak oscillations across the modes fromone to the next. By contrast, for a target in proximity to one of theends of the cavity, the corresponding wavelength or period is large,appearing as a gradual undulating curve across the modes. The wavelengthor period of the oscillations in the mode plot therefore containsinformation about the physical location of the target with respect tothe transmission line sensor.

In this transmission line implementation, resolving the target'sposition along the length of the sensor from the modal frequencydifferences can be accomplished by Fourier transform. An exampletechnique for providing the frequency-to-position function translationis the discrete FFT. FIG. 16 shows a plot 1600 illustrating relativeposition of the target or object (i.e., of the source of electromagneticabsorption and/or reflection) along the cavity's longitudinal axis 145in correspondence to the frequency difference variation with modes.

The abscissa 1610 represents this relative position, and the ordinate1620 represents deviations away from the average properties of thematerial surrounding the sensor (as lines 920 and 930 shown in FIG. 9).Idealized (i.e., absent noise) above and below peaks 1630, 1640 areplotted from the Fourier transform of the modal frequency differences.(Both non-elevated levels adjacent either side of the peaks correspondto average properties of the material surrounding the target.) The upperpeak 1630 represents the target's position near the center of thecavity. By contrast, the lower peak 1640 represents the target'sposition adjacent an edge of the cavity.

Those of ordinary skill in the art will recognize that althoughelectromagnetic waves have been described with particularity, and evenmore specifically in conjunction with the microwave portion of thespectrum, application of these principles can be extended to other wavepropagators, including acoustic signals through a material medium, andthe frequencies utilized may vary from the low kilohertz well into theGigahertz without departing from the spirit of the invention.

While certain features of the embodiments of the invention have beenillustrated as described herein, many modifications, substitutions,changes and equivalents will now occur to those skilled in the art. Itis, therefore, to be understood that the appended claims are intended tocover all such modifications and changes as fall within the true spiritof the embodiments.

1. A method for detecting an object within a defined region having alongitudinal axis, the method comprising: disposing first and secondconductive lines substantially parallel to the axis for a specifiedlength and separated from each other by a specified width, the lengthand width bounding the defined region; connecting the first and secondconductive lines with an oscillator and a shunt respectively disposed atopposite ends of the length; transmitting an electromagnetic signal fromthe oscillator through the first line at a set frequency; returning thetransmitted signal through the second line; measuring power from areflected signal by the shunt through the first line; adjusting the setfrequency based on the measured power; extracting an appropriateparameter from the reflected signal to obtain a reflectedcharacteristic; comparing the reflected characteristic to an establishedcharacteristic that lacks the object to obtain a characteristicdifferential; and analyzing the characteristic differential to obtain aposition of the object along the length.
 2. The method according toclaim 1, wherein the appropriate parameter is frequency, and comparingoperation further includes determining an offset between a firstfrequency for the reflected signal and a second frequency for theestablished signal.
 3. The method according to claim 1, wherein theparameter is photon density S_(m) and the characteristic is mode lossα_(m), being each associated with associated with the m^(th)longitudinal mode, the mode loss being related by:α_(m) = α₀ + ∫₀^(L)G(z)E_(m)(z)²𝕕z, where G is spatially dependantloss called intelligence function, E_(m) is electric field distributionof the m^(th) mode, and z is spatial interval over integral acrossreflection distance L, the photon density being related by:${S_{m} = {\frac{{nC}_{m}P_{t}}{c\left( {\alpha_{0} + \frac{L\overset{\_}{G}}{2} + {\frac{1}{2}{{\hat{G}}^{+}(\lambda)}}} \right)}\mspace{14mu}\left( {{per}{\;\mspace{11mu}}{cubic}{\;\mspace{11mu}}{meter}} \right)}},$where n is index of refraction, C_(m) is probability per unit time ofexciting a photon in the m^(th) mode, P_(t) is average transmitted radiofrequency power, c is the speed of light, α₀ is background loss, G isaverage intelligence function and Ĝ⁺ is Inverse Discrete FourierTransform of the intelligence function, the electric field distributionrelated by: ${{E_{m}(z)} = {\sin\;\frac{2\;\pi\; z}{\lambda_{m}}}},$where λ is closed circuit wavelength, and the intelligence function G issolvable by:${{G(z)} = {F\; F\;{T\left\lbrack {\frac{2\;{nC}_{m}P_{t}}{{cS}_{m}} - {2\;\alpha_{0}}} \right\rbrack}}},$where FFT designates Discrete fast-Fourier Transform operation.